If I may offer a legitimate attempt at a rebuttal, I do have an argument as to how the cases are different.
First, in the case of Charizard, it should be pointed out that Charizard was initially included as part of an "all or nothing" deal along with Squirtle and Ivysaur back in Brawl.
That being said, it was clearly no longer the case when it came to returning to Smash 4 and/or going solo and not be part of the full Pokémon Trainer gimmick.
Aside from that tiny nitpick, there is one major reason as to why including a single Starter from a given Generation of Pokémon is different from including a single Champion from Breath of the Wild.
For the most part (I am aware that there are multiple ways around this in a number of the games) only one of the Starters you pick from a set will be part of the player's adventure. Unless you're playing Yellow, you can't have Venusaur, Charizard,
and Blastoise as your companions without trading. Same with X/Y; outside of Friend Areas and trading, you can't use Chesnaut, Delphox,
and Greninja on your in-game team at the same time.
One Starter automatically becomes the most significant one of the player's personal game, while either another or both become an opponent. And not only that, but the Starters are often not treated equally in significance by both the fanbase and whoever's in charge of marketing and promotion for the overall franchise. Case in point, the reason why Charizard likely stayed while the other two were cast away with the Trainer; Charizard is CLEARLY the most significant of all three Starters from Generation 1. And while it wouldn't really be until after its Smash debut, the same would apply for Greninja as well for Generation 6.
In the case of the Champions, they are all completely
equal. One is no more significant than the other in the context of Breath of the Wild. From an in-game standpoint to a fanbase standpoint to
other material relating to the game.
There is no "clear" significant one overall. There is no "Charizard" among them. (At least to my knowledge; feel free to correct me if I'm wrong)
That's not to say that a single Champion
can't get it. Just that the Pokémon counterexample isn't necessarily the best one to use.
And that's my two cents.